Speed of Sound in Air: Examining True Statements

[leena19]

Homework Statement

Consider the following statements made regarding the speed of sound in air,
(A) Speed increases with the increase of pressure when the temperature is kept constant
(B) speed increases with the increase of temperature and humidity
(C) speed decreaes with the increase of density when the temperature is kept constant
Of the above,
1)only A is true 2) only B's true (3)only C's true 3)A & B are true (4) all A,B&C are true

Homework Equations

V=\sqrt{Bulk modulus/density}
V= \sqrt{gamma*P /d}
V=\sqrt{gamma*PV/m}
V proportional \sqrt{T}

The Attempt at a Solution

A) is wrong ,cause according to the 3rd equation,a change in pressure would also change the volume as a result V remains unchanged
B) V does increase when the temperature increases(acc. to the last equation) and also when humidity increases(as density decreases)
It is C) that I'm having a problem with,I think the speed should decrease when the density increases,even when the temperature is a constant as V is inversely proprtional to d,
But there is no answer that says both B& C are true

I don't know where I'm going wrong.
I hope someone can help.

Thank you

 

[LowlyPion]

A) is wrong because as the pressure increases, the density also increases in direct proportion to the increase in pressure.

C) For the same reason, increasing density may be identically offset (caused by) an increase in pressure.

http://en.wikipedia.org/wiki/Speed_of_sound#Dependence_on_the_properties_of_the_medium

 

[leena19]

OK,so the speed of sound depends on density only in solid and liquid media.In gases ,it depends only on molecular weight and temperature.so A and C are wrong,and in B,the speed increases in humid air only cause of the decrease in molecular weight,not because of the decrease in density.
I now understand
THANK YOU